Given: O is the center of the circle, AB is diameter and ACB is an angle inscribed in a semi-circle.
To prove: ACB = 90°
S.N | Statements | Reasons |
1 | ACB = 1/2 AOB | ACB is a circumference angle and AOB is a central angle standing on the same arc as ADB. |
2 | AOB = 180° | A straight angle. |
3 | ACB = (1/2)*180 = 90° | From statements (1) and (2), by substitution axiom |
4 | Therefore, ACB is a right angle. | From statement 3. |